Free Vibration Analysis of Functionally Graded Materials Non-uniform Beams

In this article, nonuniformity effects on free vibration analysis of functionally graded beams is discussed. variation in material properties is modeled after Powerlaw and exponential models and the non-uniformity is assumed to be exponentially varying in the width along the beams with constant thickness. Analytical solution is achieved for free vibration with simply supported conditions. It is shown that Functionally graded materials (FGM) materials property accompanying section variation with geometrical property variation has a significant effect on natural frequencies of FGM nonuniform beams. In order to show this dependency, Al/Al2O3 composite beam is modeled and the first three natural frequencies with simply supported boundary conditions is obtained for different powerlaw and exponential parameters which shows a great sensitivity to non-uniformity in different shape modes.